'''Chemical Engineering Design Library (ChEDL). Utilities for process modeling.
Copyright (C) 2016, 2017, 2018, 2019, 2020 Caleb Bell <Caleb.Andrew.Bell@gmail.com>
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
'''
from fluids.numerics import derivative, linspace
from fluids.numerics import numpy as np
from thermo.utils.functional import has_matplotlib
from thermo.utils.names import NEGLECT_P
from thermo.utils.t_dependent_property import TDependentProperty
__all__ = ['TPDependentProperty']
[docs]class TPDependentProperty(TDependentProperty):
'''Class for calculating temperature and pressure dependent chemical
properties.
On creation, a :obj:`TPDependentProperty` examines all the possible methods
implemented for calculating the property, loads whichever coefficients it
needs (unless `load_data` is set to False), examines its input parameters,
and selects the method it prefers. This method will continue to be used for
all calculations until the method is changed by setting a new method
to the to :obj:`method` attribute.
Because many pressure dependent property methods are implemented as a
low-pressure correlation and a high-pressure correlation, this class
works essentially the same as :obj:`TDependentProperty` but with extra
methods that accept pressure as a parameter.
The object also selects the pressure-dependent method it prefers.
This method will continue to be used for all pressure-dependent
calculations until the pressure-dependent method is changed by setting a
new method_P to the to :obj:`method_P` attribute.
The default list of preferred pressure-dependent method orderings is at
:obj:`ranked_methods_P`
for all properties; the order can be modified there in-place, and this
will take effect on all new :obj:`TPDependentProperty` instances created
but NOT on existing instances.
Tabular data can be provided as either temperature-dependent or
pressure-dependent data. The same `extrapolation` settings as in
:obj:`TDependentProperty` are implemented here for the low-pressure
correlations.
In addition to the methods and attributes shown here, all those from
:obj:`TPDependentProperty` are also available.
Attributes
----------
method_P : str
The method was which was last used successfully to calculate a property;
set only after the first property calculation.
method : str
The method to be used for property calculations, [-]
all_methods : set
All low-pressure methods available, [-]
all_methods_P : set
All pressure-dependent methods available, [-]
'''
P_dependent = True
interpolation_P = None
P_correlation_models = {
'Tait': {'custom': True},
}
available_P_correlations = frozenset(P_correlation_models.keys())
P_correlation_parameters = {k: k + '_parameters' for k in P_correlation_models.keys()}
P_correlation_keys_to_parameters = {v: k for k, v in P_correlation_parameters.items()}
def __init__(self, extrapolation, **kwargs):
self.tabular_data_P = {}
"""tabular_data_P, dict: Stored (Ts, Ps, properties) for any
tabular data; indexed by provided or autogenerated name."""
self.tabular_data_interpolators_P = {}
"""tabular_data_interpolators_P, dict: Stored (extrapolator,
spline) tuples which are interp2d instances for each set of tabular
data; indexed by tuple of (name, interpolation_T, interpolation_P,
interpolation_property, interpolation_property_inv) to ensure that
if an interpolation transform is altered, the old interpolator which
had been created is no longer used."""
self.P_correlations = {}
super().__init__(extrapolation, **kwargs)
self.P_limits = {}
"""Pressure limits on a per-component basis. Not currently used."""
if kwargs:
P_correlation_keys_to_parameters = self.P_correlation_keys_to_parameters
# Iterate over all the dictionaries in reverse such that the first one is left as the default
for key in reversed(list(kwargs.keys())):
if key in P_correlation_keys_to_parameters:
P_correlation_dict = kwargs.pop(key)
P_correlation_name = P_correlation_keys_to_parameters[key]
# Probably need to reverse this too
for corr_i, corr_kwargs in P_correlation_dict.items():
self.add_P_correlation(name=corr_i, model=P_correlation_name,
**corr_kwargs)
self.tabular_extrapolation_permitted = kwargs.get('tabular_extrapolation_permitted', True)
if kwargs.get('tabular_data_P', None):
for name, (Ts, Ps, properties) in kwargs['tabular_data_P'].items():
self.add_tabular_data_P(Ts, Ps, properties, name=name, check_properties=False)
method_P = kwargs.get('method_P', getattr(self, '_method_P', None))
if method_P is None:
all_methods_P = self.all_methods_P
for i in self.ranked_methods_P:
if i in all_methods_P:
method_P = i
break
self.method_P = method_P
def load_all_methods(self, load_data):
self.all_methods_P = set()
"""Set of all methods available for a given CASRN and properties;
filled by :obj:`load_all_methods`."""
self.all_methods = set()
"""Set of all P-dependent methods available for a given CASRN and properties;
filled by :obj:`load_all_methods`."""
def add_P_correlation(self, name, model, **kwargs):
d = getattr(self, model + '_parameters', None)
if d is None:
d = {}
setattr(self, model + '_parameters', d)
full_kwargs = kwargs.copy()
d[name] = full_kwargs
self.all_methods.add(name)
self.method = name
args = (kwargs['coeffs'], kwargs['N_terms'], kwargs['N_T'])
self.P_correlations[name] = args
@property
def method_P(self):
r'''Method used to set or get a specific property method.
An exception is raised if the method specified isnt't available
for the chemical with the provided information.
Parameters
----------
method : str or list
Methods by name to be considered or preferred
'''
return self._method_P
@method_P.setter
def method_P(self, method_P):
if method_P not in self.all_methods_P and method_P is not None:
raise ValueError("The given methods is not available for this chemical")
self.TP_cached = None
self._method_P = method_P
[docs] def __call__(self, T, P):
r'''Convenience method to calculate the property; calls
:obj:`TP_dependent_property <thermo.utils.TPDependentProperty.TP_dependent_property>`. Caches previously calculated value,
which is an overhead when calculating many different values of
a property. See :obj:`TP_dependent_property <thermo.utils.TPDependentProperty.TP_dependent_property>` for more details as to the
calculation procedure.
Parameters
----------
T : float
Temperature at which to calculate the property, [K]
P : float
Pressure at which to calculate the property, [Pa]
Returns
-------
prop : float
Calculated property, [`units`]
'''
if (T, P) == self.TP_cached:
return self.prop_cached
else:
if P is not None:
self.prop_cached = self.TP_dependent_property(T, P)
else:
self.prop_cached = self.T_dependent_property(T)
self.TP_cached = (T, P)
return self.prop_cached
[docs] def valid_methods_P(self, T=None, P=None):
r'''Method to obtain a sorted list of high-pressure methods that have
data available to be used. The methods are ranked in the following
order:
* The currently selected :obj:`method_P` is first (if one is selected)
* Other available pressure-depenent methods are ranked by the attribute
:obj:`ranked_methods_P`
If `T` and `P` are provided, the methods will be checked against the
temperature and pressure limits of the correlations as well.
Parameters
----------
T : float
Temperature at which to test methods, [K]
P : float
Pressure at which to test methods, [Pa]
Returns
-------
sorted_valid_methods_P : list
Sorted lists of methods valid at T and P according to
:obj:`test_method_validity_P`
'''
all_methods = self.all_methods_P
sorted_methods = [i for i in self.ranked_methods_P if i in all_methods]
current_method = self._method_P
if current_method in sorted_methods:
# Add back the user's methods to the top, in order.
sorted_methods.remove(current_method)
sorted_methods.insert(0, current_method)
if T is not None:
sorted_methods = [i for i in sorted_methods
if self.test_method_validity_P(T, P, i)]
return sorted_methods
[docs] def TP_dependent_property(self, T, P):
r'''Method to calculate the property given a temperature and pressure
according to the selected :obj:`method_P` and :obj:`method`.
The pressure-dependent method is always used and required to succeed.
The result is checked with :obj:`test_property_validity`.
If the method does not succeed, returns None.
Parameters
----------
T : float
Temperature at which to calculate the property, [K]
P : float
Pressure at which to calculate the property, [Pa]
Returns
-------
prop : float
Calculated property, [`units`]
'''
method_P = self._method_P
if method_P is None:
if self.RAISE_PROPERTY_CALCULATION_ERROR:
raise RuntimeError(f"No pressure-dependent {self.name.lower()} method selected for component with CASRN '{self.CASRN}'")
else:
return None
if self.test_method_validity_P(T, P, method_P):
try:
prop = self.calculate_P(T, P, method_P)
except: # pragma: no cover
if self.RAISE_PROPERTY_CALCULATION_ERROR:
raise RuntimeError(f"Failed to evaluate {self.name.lower()} method '{method_P}' at T={T} K and P={P} Pa for component with CASRN '{self.CASRN}'")
else:
if self.test_property_validity(prop):
return prop
elif self.RAISE_PROPERTY_CALCULATION_ERROR:
raise RuntimeError(f"{self.name} method '{method_P}' computed an invalid value of {prop} {self.units} for component with CASRN '{self.CASRN}'")
elif self.RAISE_PROPERTY_CALCULATION_ERROR:
raise RuntimeError(f"{self.name} method '{method_P}' is not valid at T={T} K and P={P} Pa for component with CASRN '{self.CASRN}'")
[docs] def TP_or_T_dependent_property(self, T, P):
r'''Method to calculate the property given a temperature and pressure
according to the selected :obj:`method_P` and :obj:`method`.
The pressure-dependent method is always tried.
The result is checked with :obj:`test_property_validity`.
If the pressure-dependent method does not succeed, the low-pressure
method is tried and its result is returned.
.. warning::
It can seem like a good idea to switch between a low-pressure and
a high-pressure method if the high pressure method is not working,
however it can cause discontinuities and prevent numerical methods
from converging
Parameters
----------
T : float
Temperature at which to calculate the property, [K]
P : float
Pressure at which to calculate the property, [Pa]
Returns
-------
prop : float
Calculated property, [`units`]
'''
if P is not None:
prop = self.TP_dependent_property(T, P)
if P is None or prop is None:
prop = self.T_dependent_property(T)
return prop
def T_atmospheric_dependent_property(self, T, P_atm=101325.0):
r'''Method to calculate the property given a temperature at the standard
atmospheric pressure to the selected :obj:`method_P` and :obj:`method`.
This is a wrapper around :obj:`TP_dependent_property`.
Parameters
----------
T : float
Temperature at which to calculate the property, [K]
P_atm : float, optional
Atmospheric pressure at which to calculate the property, [Pa]
Returns
-------
prop : float
Calculated property, [`units`]
'''
return self.TP_dependent_property(T, P_atm)
[docs] def add_tabular_data_P(self, Ts, Ps, properties, name=None, check_properties=True):
r'''Method to set tabular data to be used for interpolation.
Ts and Psmust be in increasing order. If no name is given, data will be
assigned the name 'Tabular data series #x', where x is the number of
previously added tabular data series.
After adding the data, this method becomes the selected high-pressure
method.
Parameters
----------
Ts : array-like
Increasing array of temperatures at which properties are specified, [K]
Ps : array-like
Increasing array of pressures at which properties are specified, [Pa]
properties : array-like
List of properties at `Ts` and `Ps`; the data should be indexed
[P][T], [`units`]
name : str, optional
Name assigned to the data
check_properties : bool
If True, the properties will be checked for validity with
:obj:`test_property_validity` and raise an exception if any are not
valid
'''
# Ts must be in increasing order.
if check_properties:
for p in np.array(properties).ravel():
if not self.test_property_validity(p):
raise ValueError('One of the properties specified are not feasible')
if not all(b > a for a, b in zip(Ts, Ts[1:])):
raise ValueError('Temperatures are not sorted in increasing order')
if not all(b > a for a, b in zip(Ps, Ps[1:])):
raise ValueError('Pressures are not sorted in increasing order')
if name is None:
name = 'Tabular data series #' + str(len(self.tabular_data)) # Will overwrite a poorly named series
self.tabular_data_P[name] = [Ts, Ps, properties]
self.all_methods_P.add(name)
self.method_P = name
def test_method_validity_P(self, T, P, method):
r'''Method to test the validity of a specified method for a given
temperature. Demo function for testing only;
must be implemented according to the methods available for each
individual method. Include the interpolation check here.
Parameters
----------
T : float
Temperature at which to determine the validity of the method, [K]
P : float
Pressure at which to determine the validity of the method, [Pa]
method : str
Method name to use
Returns
-------
validity : bool
Whether or not a specifid method is valid
'''
if method in self.tabular_data_P:
if self.tabular_extrapolation_permitted:
validity = True
else:
Ts, Ps, properties = self.tabular_data_P[method]
validity = Ts[0] < T < Ts[-1] and Ps[0] < P < Ps[-1]
elif method == NEGLECT_P:
return self.test_method_validity(T, self._method) if self._method else False
elif method in self.all_methods_P:
Tmin, Tmax = self.T_limits[method]
validity = Tmin < T < Tmax
else:
raise ValueError("method '%s' not valid" %method)
return validity
def interpolate_P(self, T, P, name):
r'''Method to perform interpolation on a given tabular data set
previously added via :obj:`add_tabular_data_P`. This method will create the
interpolators the first time it is used on a property set, and store
them for quick future use.
Interpolation is cubic-spline based if 5 or more points are available,
and linearly interpolated if not. Extrapolation is always performed
linearly. This function uses the transforms :obj:`interpolation_T`,
:obj:`interpolation_P`,
:obj:`interpolation_property`, and :obj:`interpolation_property_inv` if set. If
any of these are changed after the interpolators were first created,
new interpolators are created with the new transforms.
All interpolation is performed via the `interp2d` function.
Parameters
----------
T : float
Temperature at which to interpolate the property, [K]
T : float
Pressure at which to interpolate the property, [Pa]
name : str
The name assigned to the tabular data set
Returns
-------
prop : float
Calculated property, [`units`]
'''
key = (name, self.interpolation_T, id(self.interpolation_P), id(self.interpolation_property), id(self.interpolation_property_inv))
Ts, Ps, properties = self.tabular_data_P[name]
if not self.tabular_extrapolation_permitted:
if T < Ts[0] or T > Ts[-1] or P < Ps[0] or P > Ps[-1]:
raise ValueError("Extrapolation not permitted and conditions outside of range")
# If the interpolator and extrapolator has already been created, load it
if key in self.tabular_data_interpolators_P:
extrapolator, spline = self.tabular_data_interpolators_P[key]
else:
from scipy.interpolate import interp2d
if self.interpolation_T: # Transform ths Ts with interpolation_T if set
Ts2 = [self.interpolation_T(T2) for T2 in Ts]
else:
Ts2 = Ts
if self.interpolation_P: # Transform ths Ts with interpolation_T if set
Ps2 = [self.interpolation_P(P2) for P2 in Ps]
else:
Ps2 = Ps
if self.interpolation_property: # Transform ths props with interpolation_property if set
properties2 = [[self.interpolation_property(p) for p in r] for r in properties]
else:
properties2 = properties
# Only allow linear extrapolation, but with whatever transforms are specified
extrapolator = interp2d(Ts2, Ps2, properties2) # interpolation if fill value is missing
# If more than 5 property points, create a spline interpolation
if len(properties) >= 5:
spline = interp2d(Ts2, Ps2, properties2, kind='cubic')
else:
spline = None
self.tabular_data_interpolators_P[key] = (extrapolator, spline)
# Load the stores values, tor checking which interpolation strategy to
# use.
Ts, Ps, properties = self.tabular_data_P[name]
if T < Ts[0] or T > Ts[-1] or not spline or P < Ps[0] or P > Ps[-1]:
tool = extrapolator
else:
tool = spline
if self.interpolation_T:
T = self.interpolation_T(T)
if self.interpolation_P:
P = self.interpolation_P(P)
prop = tool(T, P) # either spline, or linear interpolation
if self.interpolation_property:
prop = self.interpolation_property_inv(prop)
return float(prop)
[docs] def plot_isotherm(self, T, Pmin=None, Pmax=None, methods_P=[], pts=50,
only_valid=True, show=True): # pragma: no cover
r'''Method to create a plot of the property vs pressure at a specified
temperature according to either a specified list of methods, or the
user methods (if set), or all methods. User-selectable number of
points, and pressure range. If only_valid is set,
:obj:`test_method_validity_P` will be used to check if each condition in
the specified range is valid, and :obj:`test_property_validity` will be used
to test the answer, and the method is allowed to fail; only the valid
points will be plotted. Otherwise, the result will be calculated and
displayed as-is. This will not suceed if the method fails.
Parameters
----------
T : float
Temperature at which to create the plot, [K]
Pmin : float
Minimum pressure, to begin calculating the property, [Pa]
Pmax : float
Maximum pressure, to stop calculating the property, [Pa]
methods_P : list, optional
List of methods to consider
pts : int, optional
A list of points to calculate the property at; if Pmin to Pmax
covers a wide range of method validities, only a few points may end
up calculated for a given method so this may need to be large
only_valid : bool
If True, only plot successful methods and calculated properties,
and handle errors; if False, attempt calculation without any
checking and use methods outside their bounds
show : bool
If True, displays the plot; otherwise, returns it
'''
# This function cannot be tested
if not has_matplotlib():
raise Exception('Optional dependency matplotlib is required for plotting')
import matplotlib.pyplot as plt
if Pmin is None:
if self.Pmin is not None:
Pmin = self.Pmin
else:
raise Exception('Minimum pressure could not be auto-detected; please provide it')
if Pmax is None:
if self.Pmax is not None:
Pmax = self.Pmax
else:
raise Exception('Maximum pressure could not be auto-detected; please provide it')
fig = plt.figure()
if not methods_P:
methods_P = self.all_methods_P
Ps = linspace(Pmin, Pmax, pts)
for method_P in methods_P:
if only_valid:
properties, Ps2 = [], []
for P in Ps:
if self.test_method_validity_P(T, P, method_P):
try:
p = self.calculate_P(T, P, method_P)
if self.test_property_validity(p):
properties.append(p)
Ps2.append(P)
except:
pass
plt.plot(Ps2, properties, label=method_P)
else:
properties = [self.calculate_P(T, P, method_P) for P in Ps]
plt.plot(Ps, properties, label=method_P)
plt.legend(loc='best')
plt.ylabel(self.name + ', ' + self.units)
plt.xlabel('Pressure, Pa')
plt.title(self.name + ' of ' + self.CASRN)
if show:
plt.show()
else:
return plt
[docs] def plot_isobar(self, P, Tmin=None, Tmax=None, methods_P=[], pts=50,
only_valid=True, show=True): # pragma: no cover
r'''Method to create a plot of the property vs temperature at a
specific pressure according to
either a specified list of methods, or user methods (if set), or all
methods. User-selectable number of points, and temperature range. If
only_valid is set,:obj:`test_method_validity_P` will be used to check if
each condition in the specified range is valid, and
:obj:`test_property_validity` will be used to test the answer, and the
method is allowed to fail; only the valid points will be plotted.
Otherwise, the result will be calculated and displayed as-is. This will
not suceed if the method fails.
Parameters
----------
P : float
Pressure for the isobar, [Pa]
Tmin : float
Minimum temperature, to begin calculating the property, [K]
Tmax : float
Maximum temperature, to stop calculating the property, [K]
methods_P : list, optional
List of methods to consider
pts : int, optional
A list of points to calculate the property at; if Tmin to Tmax
covers a wide range of method validities, only a few points may end
up calculated for a given method so this may need to be large
only_valid : bool
If True, only plot successful methods and calculated properties,
and handle errors; if False, attempt calculation without any
checking and use methods outside their bounds
'''
if not has_matplotlib():
raise Exception('Optional dependency matplotlib is required for plotting')
import matplotlib.pyplot as plt
if Tmin is None:
if self._T_min_any is not None:
Tmin = self._T_min_any
else:
raise Exception('Minimum temperature could not be auto-detected; please provide it')
if Tmax is None:
if self._T_max_any is not None:
Tmax = self._T_max_any
else:
raise Exception('Maximum temperature could not be auto-detected; please provide it')
if hasattr(P, '__call__'):
P_changes = True
P_func = P
else:
P_changes = False
if not methods_P:
methods_P = self.all_methods_P
Ts = linspace(Tmin, Tmax, pts)
fig = plt.figure()
for method_P in methods_P:
if only_valid:
properties, Ts2 = [], []
for T in Ts:
if P_changes:
P = P_func(T)
if self.test_method_validity_P(T, P, method_P):
try:
p = self.calculate_P(T, P, method_P)
if self.test_property_validity(p):
properties.append(p)
Ts2.append(T)
except:
pass
plt.plot(Ts2, properties, label=method_P)
else:
properties = []
for T in Ts:
if P_changes:
P = P_func(T)
properties.append(self.calculate_P(T, P, method_P))
plt.plot(Ts, properties, label=method_P)
plt.legend(loc='best')
plt.ylabel(self.name + ', ' + self.units)
plt.xlabel('Temperature, K')
plt.title(self.name + ' of ' + self.CASRN)
if show:
plt.show()
else:
return plt
[docs] def plot_TP_dependent_property(self, Tmin=None, Tmax=None, Pmin=None,
Pmax=None, methods_P=[], pts=15,
only_valid=True): # pragma: no cover
r'''Method to create a plot of the property vs temperature and pressure
according to either a specified list of methods, or user methods (if
set), or all methods. User-selectable number of points for each
variable. If only_valid is set,:obj:`test_method_validity_P` will be used to
check if each condition in the specified range is valid, and
:obj:`test_property_validity` will be used to test the answer, and the
method is allowed to fail; only the valid points will be plotted.
Otherwise, the result will be calculated and displayed as-is. This will
not suceed if the any method fails for any point.
Parameters
----------
Tmin : float
Minimum temperature, to begin calculating the property, [K]
Tmax : float
Maximum temperature, to stop calculating the property, [K]
Pmin : float
Minimum pressure, to begin calculating the property, [Pa]
Pmax : float
Maximum pressure, to stop calculating the property, [Pa]
methods_P : list, optional
List of methods to plot
pts : int, optional
A list of points to calculate the property at for both temperature
and pressure; pts^2 points will be calculated.
only_valid : bool
If True, only plot successful methods and calculated properties,
and handle errors; if False, attempt calculation without any
checking and use methods outside their bounds
'''
if not has_matplotlib():
raise Exception('Optional dependency matplotlib is required for plotting')
import matplotlib.pyplot as plt
from matplotlib.ticker import FormatStrFormatter
from numpy import ma
if Pmin is None:
if self.Pmin is not None:
Pmin = self.Pmin
else:
raise Exception('Minimum pressure could not be auto-detected; please provide it')
if Pmax is None:
if self.Pmax is not None:
Pmax = self.Pmax
else:
raise Exception('Maximum pressure could not be auto-detected; please provide it')
if Tmin is None:
if self._T_min_any is not None:
Tmin = self._T_min_any
else:
raise Exception('Minimum temperature could not be auto-detected; please provide it')
if Tmax is None:
if self._T_max_any is not None:
Tmax = self._T_max_any
else:
raise Exception('Maximum temperature could not be auto-detected; please provide it')
if not methods_P:
methods_P = self.all_methods_P
Ps = np.linspace(Pmin, Pmax, pts)
Ts = np.linspace(Tmin, Tmax, pts)
Ts_mesh, Ps_mesh = np.meshgrid(Ts, Ps)
fig = plt.figure()
ax = fig.add_subplot(1,1,1,projection="3d")
handles = []
for method_P in methods_P:
if only_valid:
properties = []
for T in Ts:
T_props = []
for P in Ps:
if self.test_method_validity_P(T, P, method_P):
try:
p = self.calculate_P(T, P, method_P)
if self.test_property_validity(p):
T_props.append(p)
else:
T_props.append(None)
except:
T_props.append(None)
else:
T_props.append(None)
properties.append(T_props)
properties = ma.masked_invalid(np.array(properties, dtype=np.float64).T)
handles.append(ax.plot_surface(Ts_mesh, Ps_mesh, properties, cstride=1, rstride=1, alpha=0.5))
else:
properties = np.array([[self.calculate_P(T, P, method_P) for T in Ts] for P in Ps])
handles.append(ax.plot_surface(Ts_mesh, Ps_mesh, properties, cstride=1, rstride=1, alpha=0.5))
ax.yaxis.set_major_formatter(FormatStrFormatter('%.4g'))
ax.zaxis.set_major_formatter(FormatStrFormatter('%.4g'))
ax.xaxis.set_major_formatter(FormatStrFormatter('%.4g'))
ax.set_xlabel('Temperature, K')
ax.set_ylabel('Pressure, Pa')
ax.set_zlabel(self.name + ', ' + self.units)
plt.title(self.name + ' of ' + self.CASRN)
plt.show(block=False)
[docs] def calculate_derivative_T(self, T, P, method, order=1):
r'''Method to calculate a derivative of a temperature and pressure
dependent property with respect to temperature at constant pressure,
of a given order using a specified method. Uses SciPy's derivative
function, with a delta of 1E-6 K and a number of points equal to
2*order + 1.
This method can be overwritten by subclasses who may perfer to add
analytical methods for some or all methods as this is much faster.
If the calculation does not succeed, returns the actual error
encountered.
Parameters
----------
T : float
Temperature at which to calculate the derivative, [K]
P : float
Pressure at which to calculate the derivative, [Pa]
method : str
Method for which to find the derivative
order : int
Order of the derivative, >= 1
Returns
-------
dprop_dT_P : float
Calculated derivative property at constant pressure,
[`units/K^order`]
'''
return derivative(self.calculate_P, T, dx=1e-6, args=[P, method], n=order, order=1+order*2)
[docs] def calculate_derivative_P(self, P, T, method, order=1):
r'''Method to calculate a derivative of a temperature and pressure
dependent property with respect to pressure at constant temperature,
of a given order using a specified method. Uses SciPy's derivative
function, with a delta of 0.01 Pa and a number of points equal to
2*order + 1.
This method can be overwritten by subclasses who may perfer to add
analytical methods for some or all methods as this is much faster.
If the calculation does not succeed, returns the actual error
encountered.
Parameters
----------
P : float
Pressure at which to calculate the derivative, [Pa]
T : float
Temperature at which to calculate the derivative, [K]
method : str
Method for which to find the derivative
order : int
Order of the derivative, >= 1
Returns
-------
dprop_dP_T : float
Calculated derivative property at constant temperature,
[`units/Pa^order`]
'''
f = lambda P: self.calculate_P(T, P, method)
return derivative(f, P, dx=1e-2, n=order, order=1+order*2)
[docs] def TP_dependent_property_derivative_T(self, T, P, order=1):
r'''Method to calculate a derivative of a temperature and pressure
dependent property with respect to temperature at constant pressure,
of a given order, according to the selected :obj:`method_P`.
Calls :obj:`calculate_derivative_T` internally to perform the actual
calculation.
.. math::
\text{derivative} = \frac{d (\text{property})}{d T}|_{P}
Parameters
----------
T : float
Temperature at which to calculate the derivative, [K]
P : float
Pressure at which to calculate the derivative, [Pa]
order : int
Order of the derivative, >= 1
Returns
-------
dprop_dT_P : float
Calculated derivative property, [`units/K^order`]
'''
try:
return self.calculate_derivative_T(T, P, self._method_P, order)
except:
pass
return None
[docs] def TP_dependent_property_derivative_P(self, T, P, order=1):
r'''Method to calculate a derivative of a temperature and pressure
dependent property with respect to pressure at constant temperature,
of a given order, according to the selected :obj:`method_P`.
Calls :obj:`calculate_derivative_P` internally to perform the actual
calculation.
.. math::
\text{derivative} = \frac{d (\text{property})}{d P}|_{T}
Parameters
----------
T : float
Temperature at which to calculate the derivative, [K]
P : float
Pressure at which to calculate the derivative, [Pa]
order : int
Order of the derivative, >= 1
Returns
-------
dprop_dP_T : float
Calculated derivative property, [`units/Pa^order`]
'''
try:
return self.calculate_derivative_P(P, T, self._method_P, order)
except:
pass
return None